Return to A Component Universe

1        Passive Components

1.1   Resistors

1.1.1      Physical Construction Of Various Resistors

Resistors are perhaps the most fundamental components and moderate the flow of current according to . Ohm, however defined this relationship in terms of current , voltage  and the length  of a piece of wire, and found a linear relationship in the DC current that was inversely proportional to the length of wire. However resistors are not so well behaved in practice.

Wire, for example has a resistance  that is temperature dependant. Most metals have a temperature dependent resistance  that is proportional to absolute temperature i.e.  where  is the resistance measured at (say) room temperature  (273 Kelvin + 25 Celsius = 298 Kelvin). The typical incandescent light bulb , for example, has a much lower “cold” resistance than when it is operating. As a result, its “in-rush” current is high until it warms up and begins to emit “black body” light.

The earliest resistors where made of spiralled up lengths of wire, and often used the metal “nichrome” as it had a much higher resistance per unit of length than other metals such as copper. These resistors were capable of dissipating large amounts of heat but due to their coil structure, also had significant inductance. “Ohms Law” then became further modified for frequency dependence as  where  became frequency dependent variables with  where  represented the associated frequency in Hz.

Eventually people realised that large resistor values made of metal became impractical due to the long lengths of skinny wire required, and also that the RF properties were abysmal. Even at audio frequencies, a 1 Meg-Ohm resistor made of wire would not have had its DC value. A better element needed to be found.

This is where Carbon soon became the Holy Grail of resistors. A thin surface of a carbon-based mixture was first spread over a ceramic tube and wire attachments where wrapped around each end to become its electrodes. The resulting structure was then covered in an annealing paint and fired in an oven. For reasons perhaps unfathomable, the resistor adopted a colour coded resistance value scheme that was based on two prefix values and a multiplier,

	Resistor values were expressed as a body colour value, followed by a second end digit colour and then a dot to represent a multiplying exponent.   In this example, the body colour is red = 2, the end colour is black = 0, and the multiplier colour is yellow = 4.   Putting it together, this resistor “Ohmic” value would be   “2 + 0” * 10^4 = 20 * 10,000 = 200,000 Ohms.

 

Colour	Number
Black	0
Brown	1
Red	2
Orange	3
Yellow	4
Green	5
Blue	6
Violet	7
Grey	8
White	9

(The available range of resistor values (as well as that of other passive components) was “quantized” into equal percentage increments called the “E-12” series. Within each decade these defined values were 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8 and 8.2. The double mantissa remains today but further refined graduations can be obtained in E-24 etc series.)

This component body style adopted was designed to suit the broadcast radio’s of the day, all of which used Valves, and the resistors were required to dissipate several watts of heat, and be non inductive, at least at the relatively low frequencies of medium wave (550 - 1650 kHz) radio. Military applications, fuelled by the two World wars sought similar constructions. But people like their space, and large broadcast radios, although being a nice fashion piece, loose their appeal when portability is required, especially on a battle-field. Small size, low battery current drain and easy transportability became the driver towards a better class of resistor.  

Valves where the favourite technology of the time and used to come in octal base mountings  and required a +230 V anode supply at 5 to 50 mA of current. People looked towards a more energy efficient solution. Smaller valves were made, operating at lower voltages and currents and with high mechanical precision for cathode, grid and anode structure placements. At their zenith, the vacuum valve could sit on less than a quarter of a thumb, and operate from a 12 V battery with less than 1 mA of anode current. But where was the resistor in all of this? That old-fashioned bulky construction was many times larger than the vacuum valve device that required is current from voltage regulation! 

Resistors had to be made smaller, still based on a carbon element, ceramic body and flying lead attachments. They no longer needed to dissipate large amounts of heat and as people moved into short-wave radio (2 ~ 30 MHz) smaller size gave an added bonus of reduced parasitic inductance (approximately 1 nH per mm of length). The humble resistor was simply adapted to a size-shrunk version of the previous with end caps replacing the wrap and contact wire terminals.

	This resistor style became all the rage in the 1950’s onwards. It was cheap, easy to manufacture and adopted the familiar colour value scheme of its predecessors. It also included a tolerance attribute – silver was +/-10 % and gold was +/- 5%

 

Sadly, the leaded resistor remained a monument of strength well through the labour intensive days of mass production for the public and the military. However it needed PCB’s to be drilled, people or machines to stick its stalk leaded attachments through, and yet another process to snip the overhanging nonsense off just the be able to bath in the electrically soothing bath of a hot solder wave flow process.

It was at this point the Surface Mount PCB revolution began. No more would manufacturers stand for labour intensive product fabrication processes. “If it can’t be done by a machine, it shouldn’t be done at all”. The enemy of productivity was the lead. So why not leave them off and go for a planar mount structure?

1.1.2      The RF Properties Of Resistors

These resistors are suitable for low power application (D_issipation  < 62 mW !) and have low lead inductance, usually less than 1 nH, especially when mounted on low substrate height PCB’s. But what about the higher power needs?

“Free air” resistors have an equivalent circuit model that approximates the following topology,

	Leaded resistors have a parasitic inductance of about 1 nH per mm of body and lead length, and a “fringing” parallel capacitance of about 0.2 pF.

 

However what is the equivalent Surface Mount Device (SMD) equivalent model? One possible suggestion is to consider it as a micro-stripline element with a defined resistance per unit length based on its geometry,

We would then consider the resistor as a lossy transmission line as described by the following distributed circuit,

In this case,  represent parameters per unit length, and the resulting structure could now be viewed as a transmission line. For the purpose of modelling the resistor, the following approximation is suggested,

However there is a slight complication. The substrate consists of two media, one consisting of printed circuit board material, and the other consisting of the resistor’s insulating body. The height of the top carbon compound layer above the ground plane is H + h. However what is the effective relative permitivity  between these two conducting surfaces?

To answer this question we consider the two media to represent capacitors in series. Each has a capacitance proportional to their relative permittivity  and , and inversely proportional to each substrate’s height h and H. This suggests that  and  for some constant  depending on physical geometries of L and W. The total capacitance  is then given by . We will now propose that their exists an equivalent composite permittivity  that would predict the same total capacitance  given the total separation  . This implies,

Substituting  and  we can show that

This total composite permittivity  can then be used in standard circuit simulation models for the micro-stripline approximation described.

1.1.3      The Noise Properties Of Resistors

Still, resistance as it stands also does more than just obey Ohm’s Law – it is a maverick for generating noise sources of its own. All resistors, given thermal agitation, have a noise signal of their own to speak. The noise power quantity of their message is . This is considered to have a constant spectral density  with frequency .

So how much noise voltage would appear across, say, a 50-Ohm resistor at 25 C room temperature? Since  or in dBm units of power,

Note that the –30 term is added to return us to units of Watts (dBW) from the more common use of milli-Watts (dBm). Some interesting predictions can be made

Noise voltage is proportional to the square root of resistance and the square root to the measurement bandwidth. The hypothetical 1,000,000,000,000 ohm resistor (1 Meg Meq Ohm) would actually generate almost as much RMS voltage as a small 9 V radio battery if measured in a 100 MHz bandwidth ! What if the resistor could be made even larger – or if we simply increased the bandwidth – would its terminal voltage become so high that it could it arc over, or worse, could it even electrocute you? And then, what about an open circuit – its resistance is defined to be infinite, so does that imply an infinite noise voltage also?

To find answers to this seeming paradox please read the Appendix chapter “What Pulls The Reigns On Resistive Noise?”

1.1.4      Beware The Non Linear Properties Of Real Resistors

Various resistive structures are used for RF power amplifier terminations, used for communications product testing. These are available up to 500 Watts power rating and can either be a simple 50-Ohm (etc) termination or constructed as a x-dB 50 (or 75) Ohm attenuator “PAD”.

A high power, resistors may not obey Ohm’s Law very well, and may give rise to unwanted artefacts. For example, a 100 Watt sinusoid, applied to a 500 Watt 20 dB attenuator, may exhibit harmonic levels at –70 dB, even if the input is harmonic free! If a transmitters harmonic spurious output needs to be measured, it is better to use a directional coupler and a termination load. These loads tend to generate far less harmonic energy than an attenuation PAD.

High RF currents can cause harmonic currents to flow in attenuator pads. A directional coupler can be used to provide much greater dynamic range.

1.2   Capacitors

1.2.1      Capacitor Physics

According to my very old physics “Sears, Zemansky and Young”, book, those good old Greeks knew all about static electricity all the way shot back into the 600 BC. They found that rubbing pieces of amber (goo from trees as an isolator) on fur (from an animal) that small and light objects could be picked up. Although they didn’t know it at the time, Charles Augustin de Coloumb (1736 - 1806) would eventually come up with some law saying

where  was the attracting force in Newtons,  was some scaling constant known in scientifically polite circles to be   ( being another defined quantity about the speed of light in ) and  being each objects “charge” separated by a distance in meters .

So you could rob an old stick of amber from some dead tree on your sleeve and pick up bits of paper – were is the use in that? At the time, nobody had even heard of Newton, nor Coulomb, Gauss or Einstein. Still the Greeks back then coined a phrase for “atomos” meaning “indivisible” and “elektron” meaning amber.

Well so began the birth of the Atom and the Electron, even back then in the hurly girly days of solidified seepages from trees and rubbing on fur. Little did they know about sub atomic particles back then, but still the quest for electronic knowledge continued. 

I guess at the time people had many instances to observe the forces of electricity – not just in the sparks that could be rubbed from the pet cat’s back but in the atmospheric discharges we call Lightening.

Here is a depiction about the capacity of an electron flow could come about,

Well that is perhaps a bit fanciful, would dinosaurs care less if a tree went on

fire if no-one was on a beach bench to see it? At this point we come to the famous “Leydon-Jar”.

1.2.2      Capacitor Construction

This point is history could go back to the Egyptians trying to trap light in a knotted wood basket. They would open the lid (as in the urban legend) in the path of the sun’s smiling rays, and close it quickly hoping to capture a little bit of its essence. Sadly, even inside the darkest corridors of their Sphinx or Pyramids, the opened wicker basket failed to glow. Instead the trapped light had out thwarted their very plans of capture, and they were left in the dark!

Well light was elusive, but electrons were far more easily caught. The Leydon Jar formed a primitive but high voltage capacitor that could be used to store static electricity. After the charge, its terminals could be shorted and tiny sparks could be seen.

People in the 18^th century realised conductors and their role in the flow of electricity, but how could current flow through the insulation of a capacitor? Initially they imagined the electrons somehow “condensed” through the insulating glass material, and called the resulting component a “condenser”. This terminology persisted well past the 1940’s until the mechanisms of charge became clearer, and the concept of “charge storage” replaced the definition of a “condenser” with the more correct terminology of “capacitor”. In honour of Michael Faraday the unit of capacitance was called the “Farad” and related capacitance , voltage  and stored charge  to the equation

It wasn’t long before every man, women and their dog wanted a piece of capacitor action. The old big and clumsy Leydon Jar wasn’t well received in electronic circles. Your more sophisticated electronics pioneer wanted pre-made capacitor components for their experiments, and to make circuit gizmos that people would then buy and use. A better construction was called for, with issues such as mechanical rigidity, reproducibility, size and voltage tolerance high on people’s agendas.

Faraday had found a simple relationship between Capacitance and planar geometry given by

He then went on to find that some insulating materials could be placed between the plates to yield even higher capacitance for a given geometry.

1.2.3      Multiple Plate Capacitors

Recent SMD Ceramic stacked plate capacitors can be found with capacitance values greater than 10 uF. The actual Ceramic comes in many grades, depending on permitivitty. “NPO” types have low permitivitty, good temperature stability and low RF loss. Higher permitivity materials such as X7R are also used, mainly for supply decoupling. These can be “microphonic” as higher grade ceramics tend to be peizo-electric. Small component vibrations caused by Fans, speakers or other movement can then be translated into audio voltages that appear as unwanted audible noise.

1.2.3.1    Cylindrical Foil Capacitors

The first cylindrical capacitor was probably the “Leydon Jar”. This was followed by stacked plate capacitors based on Mica. However the assembly techniques would have been time intensive as each plate would be stacked one at a time. The idea of a cylindrical construction, based on two rolls of metal foil and a flexible separating dielectric became popular. Paper was an extremely low cost dielectric and Aluminium foil provided the plates.

1.2.3.2    Electrolytic Capacitors

Cylindrical capacitors were relatively inexpensive and easy to manufacture, but were limited to relatively low values of capacitance, usually less than 1 uF.  

The search for that elusive high permittivity dielectric continued. Large value capacitors were needed for high voltage AC to DC power supply filtering , and values much greater then  1 uF were sought. some compounds were known to have high relative permittivity, water being one and Aluminium oxide being another. The “electrolytic” capacitor combined both – aluminium foil was allowed to develop a very thin oxide surface in air, which became the main dielectric. Again, a cylindrical construction was used with water inserted to make a uniform electrical contact. The result was a very high density capacitor with good voltage handling capability. However the need to retain the oxide layer required the capacitor to be polarised, - if reversed the oxide would be reduced to the aluminium base metal and a shorted capacitor would result.

In some cases this effect was used to create a rectifier – AC could be converted to pulsing DC based on the asymmetrical conduction properties. Some early car battery chargers used this principle.

Today’s electrolytic capacitors achieve extremely good capacity and voltage densities. 10,000 uF components at 63 V are commonplace. However beware low temperatures – when the water freezes, the connection to the oxide may be lost. Electrolytic capacitors can make very poor components at temperatures below 0 C. However the “Dry Electrolytic” variation overcomes this limitation. In addition, the use of alternative dielectrics, such as Tantalum Oxide also offers superior performance.

1.3   Inductors

Inductance is a quantity that relates the rate of change of current to voltage, i.e.